search tree in scala - sorting

Question

I'm trying to put my first steps into Scala, and to practice I took a look at the google code jam storecredit excersize. I tried it in java first, which went well enough, and now I'm trying to port it to Scala. Now with the java collections framework, I could try to do a straight syntax conversion, but I'd end up writing java in scala, and that kind of defeats the purpose. In my Java implementation, I have a PriorityQueue that I empty into a Deque, and pop the ends off untill we have bingo. This all uses mutable collections, which give me the feeling is very 'un-scala'. What I think would be a more functional approach is to construct a datastructure that can be traversed both from highest to lowest, and from lowest to highest. Am I on the right path? Are there any suitable datastructures supplied in the Scala libraries, or should I roll my own here?
EDIT: full code of the much simpler version in Java. It should run in O(max(credit,inputchars)) and has become:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
public class StoreCredit {
private static BufferedReader in;
public static void main(String[] args) {
in = new BufferedReader(new InputStreamReader(System.in));
try {
int numCases = Integer.parseInt(in.readLine());
for (int i = 0; i < numCases; i++) {
solveCase(i);
}
} catch (IOException e) {
e.printStackTrace();
}
}
private static void solveCase(int casenum) throws NumberFormatException,
IOException {
int credit = Integer.parseInt(in.readLine());
int numItems = Integer.parseInt(in.readLine());
int itemnumber = 0;
int[] item_numbers_by_price = new int[credit];
Arrays.fill(item_numbers_by_price, -1); // makes this O(max(credit,
// items)) instead of O(items)
int[] read_prices = readItems();
while (itemnumber < numItems) {
int next_price = read_prices[itemnumber];
if (next_price <= credit) {
if (item_numbers_by_price[credit - next_price] >= 0) {
// Bingo! DinoDNA!
printResult(new int[] {
item_numbers_by_price[credit - next_price],
itemnumber }, casenum);
break;
}
item_numbers_by_price[next_price] = itemnumber;
}
itemnumber++;
}
}
private static int[] readItems() throws IOException {
String line = in.readLine();
String[] items = line.split(" "); // uh-oh, now it's O(max(credit,
// inputchars))
int[] result = new int[items.length];
for (int i = 0; i < items.length; i++) {
result[i] = Integer.parseInt(items[i]);
}
return result;
}
private static void printResult(int[] result, int casenum) {
int one;
int two;
if (result[0] > result[1]) {
one = result[1];
two = result[0];
} else {
one = result[0];
two = result[1];
}
one++;
two++;
System.out.println(String.format("Case #%d: %d %d", casenum + 1, one,
two));
}
}

Answer 1

I'm wondering what you are trying to accomplish using sophisticated data structures such as PriorityQueue and Deque for a problem such as this. It can be solved with a pair of nested loops:
for {
i <- 2 to I
j <- 1 until i
if i != j && P(i-1) + P(j - 1) == C
} println("Case #%d: %d %d" format (n, j, i))
Worse than linear, better than quadratic. Since the items are not sorted, and sorting them would require O(nlogn), you can't do much better than this -- as far as I can see.
Actually, having said all that, I now have figured a way to do it in linear time. The trick is that, for every number p you find, you know what its complement is: C - p. I expect there are a few ways to explore that -- I have so far thought of two.
One way is to build a map with O(n) characteristics, such as a bitmap or a hash map. For each element, make it point to its index. One then only has to find an element for which its complement also has an entry in the map. Trivially, this could be as easily as this:
val PM = P.zipWithIndex.toMap
val (p, i) = PM find { case (p, i) => PM isDefinedAt C - p }
val j = PM(C - p)
However, that won't work if the number is equal to its complement. In other words, if there are two p such that p + p == C. There are quite a few such cases in the examples. One could then test for that condition, and then just use indexOf and lastIndexOf -- except that it is possible that there is only one p such that p + p == C, in which case that wouldn't be the answer either.
So I ended with something more complex, that tests the existence of the complement at the same time the map is being built. Here's the full solution:
import scala.io.Source
object StoreCredit3 extends App {
val source = if (args.size > 0) Source fromFile args(0) else Source.stdin
val input = source getLines ()
val N = input.next.toInt
1 to N foreach { n =>
val C = input.next.toInt
val I = input.next.toInt
val Ps = input.next split ' ' map (_.toInt)
val (_, Some((p1, p2))) = Ps.zipWithIndex.foldLeft((Map[Int, Int](), None: Option[(Int, Int)])) {
case ((map, None), (p, i)) =>
if (map isDefinedAt C - p) map -> Some(map(C - p) -> (i + 1))
else (map updated (p, i + 1), None)
case (answer, _) => answer
}
println("Case #%d: %d %d" format (n, p1, p2))
}
}